
as the Fourier transformed order parameter with respect to the relative coordinate of the Cooper pair.
In \(\Delta ({\mathbf {k}_{\rm F}},{\mathbf {r}})\) , the \({\mathbf {k}_{\rm F}}\)  dependence represents the orbital symmetry of the Cooper pair,
while the slowly varying \({\mathbf {r}}\)  dependence represents the spatial dependence of the order parameter
in terms of the center of mass coordinate.
Then, we obtain the following equation of motion of the field operators:
[1]}
\(&\frac{\partial }{\partial \tau }\left(\begin{matrix}\psi _{{\mathbf {k}_{\rm F}}\uparrow }({\mathbf {r}},\tau ) \cr \psi _{-{\mathbf {k}_{\rm F}}\downarrow }^\dagger ({\mathbf {r}},\tau )\end{matrix}\right) \cr &= -\left(\begin{matrix}- {\rm i}{\mathbf {v_{\rm F}}}\cdot \nabla & \Delta ({\mathbf {k}_{\rm F}},{\mathbf {r}}) \cr \Delta ({\mathbf {k}_{\rm F}},{\mathbf {r}}) & {\rm i}{\mathbf {v_{\rm F}}}\cdot \nabla \end{matrix}\right)\left(\begin{matrix}\psi _{{\mathbf {k}_{\rm F}}\uparrow }({\mathbf {r}},\tau ) \cr \psi _{-{\mathbf {k}_{\rm F}}\downarrow }^\dagger ({\mathbf {r}},\tau )\end{matrix}\right),\) 
